| sin(α + β) | sinαcosβ+cosαsinβ | Addition formula for sine - expands compound angles into basic functions |
| cos(α + β) | cosαcosβ−sinαsinβ | Addition formula for cosine - note the subtraction in the expansion |
| tan(α + β) | 1−tanαtanβtanα+tanβ | Addition formula for tangent - undefined when denominator equals zero |
| csc(α + β) | cscαcotβ+cotαcscβcscαcscβ | Reciprocal of sine sum - derived from basic addition formula |
| sec(α + β) | secαcotβ−tanαsecβsecαsecβ | Reciprocal of cosine sum - complex form for advanced calculations |
| cot(α + β) | cotβ+cotαcotαcotβ−1 | Addition formula for cotangent - derived from tangent sum formula |